To find the greatest common factor (GCF) of the expression \(18j + 27\), we can first identify the coefficients of the terms in the expression, which are 18 and 27.
- Find the GCF of the coefficients:
- The factors of 18 are: \(1, 2, 3, 6, 9, 18\).
- The factors of 27 are: \(1, 3, 9, 27\).
- The common factors are: \(1, 3, 9\).
The greatest common factor from these is \(9\).
- Factor the expression:
- We can also express the terms in factored form using the GCF: \[ 18j + 27 = 9(2j + 3) \] This confirms that the GCF is indeed \(9\).
Thus, the GCF of \(18j + 27\) is 9.